report-b8d1484d7dbf.utf8.md

RFM for Bookbinders

Loading the data …

bbb <- readr::read_rds("data/bbb.rds")
register("bbb")

Assessing recency

visualize(
  bbb, 
  xvar = "last", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Months since last purchase (last)"
  ),
  custom = FALSE
)

Creating the recency variable rec_iq using the following command in Data > Transform:

rec_iq = xtile(last, 5)

## create new variable(s)
bbb <- mutate(bbb, rec_iq = xtile(last, 5))

Does recency predict purchase? Are the best customers in quintile 1? The graph below shows this is indeed the case.

visualize(
  bbb, 
  xvar = "rec_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Recency quintiles (rec_iq)"
  ),
  custom = FALSE
)

Assessing frequency

Plots shows that purchase probility is NOT highest in the 1st quantile for frequencey (purch).

visualize(
  bbb, 
  xvar = "purch", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Purchase frequency (purch)"
  ),
  custom = FALSE
)

This means we need to ‘flip’ the bin numbers so the highest purchase probility is in the 1st bin (quantile). The easiest way to do this is to add rev = TRUE in the call to xtile.

freq_iq = xtile(purch, 5, rev = TRUE)

Alternatively, you could use:

freq_iq = 6L - xtile(purch, 5)

## bin variables
bbb <- mutate(bbb, freq_iq = xtile(purch, 5, rev = TRUE))

visualize(
  bbb, 
  xvar = "freq_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Frequency quintiles (freq_iq)"
  ),
  custom = FALSE
)

Why are there only 4 values? Looking at the histogram below we see that the distribution of purch is heavily skewed (to the right). This makes it difficult to create 5 bins of similar size

visualize(bbb, xvar = "purch", color = "freq_iq")

Assessing monetary value

The plot shows that purchase probility is NOT highest in the 1st quantile for monetary (total)

visualize(
  bbb, 
  xvar = "total", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Monetary value (total)"
  ), 
  custom = TRUE
) + 
  theme(axis.ticks = element_blank(), axis.text.x = element_blank())

Just like we did for frequency we have to ‘flip’ quantiles so the highest purchase probility is in the 1st quantile (i.e., add rev = TRUE)

mon_iq = xtile(total, 5, rev = TRUE)

## bin variables
bbb <- mutate(bbb, mon_iq = xtile(total, 5, rev = TRUE))

visualize(
  bbb, 
  xvar = "mon_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Monetary value quantiles (mon_iq)"
  ),
  custom = FALSE
)

Create the RFM index

Use Data > Transform > Create to generate the RFM index

rfm_iq = paste0(rec_iq, freq_iq, mon_iq)

## create new variable(s)
bbb <- mutate(bbb, rfm_iq = paste0(rec_iq, freq_iq, mon_iq))

visualize(
  bbb, 
  xvar = "rfm_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Independent RFM index (rfm_iq)"
  ),
  custom = TRUE
) + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  geom_hline(yintercept = 1/9)

Generate sequential N-tile

## create new variable(s)
bbb <- group_by(bbb, rec_iq) %>% 
  mutate(freq_sq = xtile(purch, 5, rev = TRUE)) %>% 
  ungroup()

## create new variable(s)
bbb <- group_by(bbb, rec_iq, freq_sq) %>% 
  mutate(mon_sq = xtile(total, 5, rev = TRUE)) %>% 
  ungroup()

visualize(
  bbb, 
  xvar = "freq_sq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Frequency quintiles (freq_sq)"
  ),
  custom = FALSE
)

visualize(
  bbb, 
  xvar = "freq_sq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Frequency quintiles (freq_sq)"
  ),
  custom = FALSE
)

visualize(
  bbb, 
  xvar = "mon_sq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Monetary value quintiles (mon_sq)"
  ),
  custom = FALSE
)

Generate Sequential RFM index

Use Data > Transform > Create to generate the RFM index

rfm_sq = paste0(rec_iq, freq_sq, mon_sq)

## create new variable(s)
bbb <- mutate(bbb, rfm_sq = paste0(rec_iq, freq_sq, mon_sq))

visualize(
  bbb, 
  xvar = "rfm_sq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'",
    x =  "Sequential RFM index (rfm_sq)"
  ),
  custom = TRUE
) + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1))  +
  geom_hline(yintercept = 1/9)

Resonse rate without RFM

result <- explore(
  bbb, 
  vars = "buyer", 
  fun = c("n_obs", "mean", "min", "max")
)
summary(result, top = "fun", dec = 4)

Explore
Data        : bbb 
Functions   : n_obs, mean, min, max 
Top         : Function 

 variable  n_obs   mean min max
    buyer 50,000 0.0904   0   1

Break-even (aggr)

The breakeven value is 11.11%. All cells above the breakeven line in the plot below will be mailed.

visualize(
  bbb, 
  xvar = "rfm_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Independent RFM index (rfm_iq)"
  ),
  custom = TRUE
) + 
  geom_hline(aes(yintercept = breakeven)) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1))

Resonse rate

Now that we are creating variables to use in targeting we should use the training variable.

Create the mailto_iq variable for independent RFM

mailto_iq = mean(buyer == "yes") > 1/9

## mail TRUE or FALSE
bbb <- group_by(bbb, rfm_iq) %>% 
  mutate(mailto_iq = (sum(training == 1 & buyer == "yes") / sum(training == 1)) > breakeven) %>% 
  ungroup()

## also calculate response rate per group as an illustration
bbb <- group_by(bbb, rfm_iq) %>% 
  mutate(rfm_iq_resp = sum(training == 1 & buyer == "yes") / sum(training == 1)) %>% 
  ungroup()

result <- pivotr(
  bbb, 
  cvars = c("mailto_iq", "training"), 
  fun = "n_obs", 
  normalize = "column"
)
summary(result, dec = 2, perc = TRUE)

Pivot table
Data        : bbb 
Categorical : mailto_iq training 
Normalize by: column 

 training  FALSE.   TRUE.   Total
        0  29.83%  30.31%  30.00%
        1  70.17%  69.69%  70.00%
    Total 100.00% 100.00% 100.00%

result <- explore(
  bbb, 
  vars = "buyer", 
  byvar = c("training", "mailto_iq"), 
  fun = c("n_obs", "mean")
)
summary(result, dec = 4)

Explore
Data        : bbb 
Grouped by  : training mailto_iq 
Functions   : n_obs, mean 
Top         : Function 

 training mailto_iq variable  n_obs   mean
        0     FALSE    buyer  9,704 0.0542
        0      TRUE    buyer  5,296 0.1531
        1     FALSE    buyer 22,823 0.0561
        1      TRUE    buyer 12,177 0.1564

Calculate profits and ROME

dat <- filter(bbb, training == 0)
perc_mail = mean(dat$mailto_iq)
nr_mail = 500000 * perc_mail
rep_rate <- filter(dat, mailto_iq == TRUE) %>% 
  summarize(rep_rate = mean(buyer == "yes")) %>%
  pull("rep_rate")
nr_resp = nr_mail * rep_rate 
mail_cost = 1 * nr_mail 
profit = 9 * nr_resp - mail_cost
ROME = profit / mail_cost

Based on independent RFM the number of customers BBB should mail is 176,533 (35.31%). The response rate for the selected customers is predicted to be 15.31% or 27,033 buyers. The expected profit is $66,767. The mailing cost is estimated to be $176,533 with a ROME of 37.82%

Repsonse rate with sequential RFM

Create the mailto_sq variable for sequential RFM

mailto_sq = mean(buyer == "yes") > 1/9

## mail TRUE or FALSE
bbb <- group_by(bbb, rfm_sq) %>% 
  mutate(mailto_sq = (sum(training == 1 & buyer == "yes") / sum(training == 1)) > breakeven) %>% 
  ungroup()

## also calculate response rate per group as an illustration
bbb <- group_by(bbb, rfm_sq) %>% 
  mutate(rfm_sq_resp = sum(training == 1 & buyer == "yes") / sum(training == 1)) %>% 
  ungroup()

result <- pivotr(
  bbb, 
  cvars = c("mailto_iq", "training"), 
  fun = "n_obs", 
  normalize = "column"
)
summary(result, dec = 2, perc = TRUE)

Pivot table
Data        : bbb 
Categorical : mailto_iq training 
Normalize by: column 

 training  FALSE.   TRUE.   Total
        0  29.83%  30.31%  30.00%
        1  70.17%  69.69%  70.00%
    Total 100.00% 100.00% 100.00%

result <- explore(
  bbb, 
  vars = "buyer", 
  byvar = c("training", "mailto_iq"), 
  fun = c("n_obs", "mean")
)
summary(result, dec = 4)

Explore
Data        : bbb 
Grouped by  : training mailto_iq 
Functions   : n_obs, mean 
Top         : Function 

 training mailto_iq variable  n_obs   mean
        0     FALSE    buyer  9,704 0.0542
        0      TRUE    buyer  5,296 0.1531
        1     FALSE    buyer 22,823 0.0561
        1      TRUE    buyer 12,177 0.1564

Calculate profits and ROME

dat <- bbb
perc_mail = mean(dat$mailto_sq)
nr_mail = 500000 * perc_mail
rep_rate <- filter(dat, mailto_sq == TRUE) %>% 
  summarize(rep_rate = mean(buyer == "yes")) %>%
  pull("rep_rate")
nr_resp = nr_mail * rep_rate 
mail_cost_sq = 1 * nr_mail 
profit_sq = 9 * nr_resp - mail_cost_sq
ROME_sq = profit_sq / mail_cost_sq

Based on sequential RFM the number of customers BBB should mail is 166,980 (33.40%). The response rate for the selected customers is predicted to be 15.80% or 26,390 buyers. The expected profit is $70,530. The mailing cost is estimated to be $166,980 with a ROME of 42.24%.

Compare this to the main results from independent RFM. The expected profit is $66,767. The mailing cost is estimated to be $176,533 with a ROME of 37.82%

Confirming the break-even response rate

If we select the predicted response rate for both of the rfm indices (i.e., rfm_iq_resp and rfm_iq_resp), and select a profit and ROME plot in Model > Evaluate Classification you should see the plots below. A visual inspection suggests that profits will be maximized if we target the top 35% of customers (approximately). You already calculated the exact percentages above. You should find that the number you calculated is very similar to the numbers highlighted green in the performance.xls file on Dropbox.

result <- evalbin(
  bbb, 
  pred = c("rfm_iq_resp", "rfm_sq_resp"), 
  rvar = "buyer", 
  lev = "yes", 
  qnt = 50, 
  margin = 9, 
  train = "Test", 
  data_filter = "training == 1"
)
summary(result, prn = FALSE)

Evaluate predictions for binary response models
Data        : bbb 
Filter      : training == 1 
Results for : Test 
Predictors  : rfm_iq_resp, rfm_sq_resp 
Response    : buyer 
Level       : yes in buyer 
Bins        : 50 
Cost:Margin : 1 : 9

plot(result, plots = "profit", custom = FALSE)

Using the RFM index in a logistic regression

result <- logistic(
  bbb, 
  rvar = "buyer", 
  evar = "rfm_sq", 
  lev = "yes",
  data_filter = "training == 1"
)
summary(result)

Logistic regression (GLM)
Data                 : bbb
Filter               : training == 1
Response variable    : buyer
Level                : yes in buyer
Explanatory variables: rfm_sq 
Null hyp.: there is no effect of rfm_sq on buyer
Alt. hyp.: there is an effect of rfm_sq on buyer

                OR coefficient std.error z.value p.value    
 (Intercept)            -1.083     0.144  -7.548  < .001 ***
 rfm_sq|112  0.941      -0.061     0.202  -0.300   0.764    
 rfm_sq|113  0.903      -0.103     0.211  -0.487   0.626    
 rfm_sq|114  0.807      -0.214     0.211  -1.015   0.310    
 rfm_sq|115  0.826      -0.191     0.213  -0.900   0.368    
 rfm_sq|121  0.609      -0.496     0.208  -2.381   0.017 *  
 rfm_sq|122  0.642      -0.444     0.209  -2.126   0.033 *  
 rfm_sq|123  0.513      -0.668     0.215  -3.111   0.002 ** 
 rfm_sq|124  0.694      -0.365     0.204  -1.790   0.073 .  
 rfm_sq|125  0.644      -0.439     0.202  -2.172   0.030 *  
 rfm_sq|131  0.502      -0.690     0.388  -1.778   0.075 .  
 rfm_sq|132  0.591      -0.526     0.392  -1.342   0.180    
 rfm_sq|133  0.568      -0.566     0.374  -1.512   0.130    
 rfm_sq|134  0.543      -0.611     0.390  -1.568   0.117    
 rfm_sq|135  1.092       0.088     0.318   0.276   0.783    
 rfm_sq|141  0.525      -0.645     0.192  -3.366  < .001 ***
 rfm_sq|142  0.543      -0.610     0.193  -3.160   0.002 ** 
 rfm_sq|143  0.427      -0.851     0.198  -4.290  < .001 ***
 rfm_sq|144  0.419      -0.870     0.201  -4.336  < .001 ***
 rfm_sq|145  0.417      -0.875     0.200  -4.378  < .001 ***
 rfm_sq|151  0.472      -0.751     0.196  -3.832  < .001 ***
 rfm_sq|152  0.355      -1.036     0.208  -4.972  < .001 ***
 rfm_sq|153  0.413      -0.885     0.201  -4.410  < .001 ***
 rfm_sq|154  0.317      -1.149     0.210  -5.468  < .001 ***
 rfm_sq|155  0.393      -0.934     0.204  -4.582  < .001 ***
 rfm_sq|211  0.793      -0.232     0.206  -1.125   0.261    
 rfm_sq|212  0.694      -0.365     0.212  -1.724   0.085 .  
 rfm_sq|213  0.572      -0.559     0.221  -2.526   0.012 *  
 rfm_sq|214  0.828      -0.189     0.205  -0.921   0.357    
 rfm_sq|215  0.633      -0.457     0.211  -2.170   0.030 *  
 rfm_sq|221  0.445      -0.810     0.224  -3.620  < .001 ***
 rfm_sq|222  0.625      -0.469     0.215  -2.180   0.029 *  
 rfm_sq|223  0.565      -0.570     0.224  -2.541   0.011 *  
 rfm_sq|224  0.464      -0.768     0.226  -3.400  < .001 ***
 rfm_sq|225  0.253      -1.375     0.264  -5.199  < .001 ***
 rfm_sq|241  0.236      -1.444     0.235  -6.133  < .001 ***
 rfm_sq|242  0.282      -1.265     0.221  -5.731  < .001 ***
 rfm_sq|243  0.301      -1.202     0.219  -5.478  < .001 ***
 rfm_sq|244  0.198      -1.620     0.248  -6.525  < .001 ***
 rfm_sq|245  0.338      -1.085     0.212  -5.124  < .001 ***
 rfm_sq|251  0.279      -1.276     0.226  -5.651  < .001 ***
 rfm_sq|252  0.304      -1.192     0.218  -5.471  < .001 ***
 rfm_sq|253  0.254      -1.371     0.231  -5.927  < .001 ***
 rfm_sq|254  0.209      -1.563     0.240  -6.518  < .001 ***
 rfm_sq|255  0.176      -1.738     0.254  -6.830  < .001 ***
 rfm_sq|311  0.551      -0.596     0.207  -2.873   0.004 ** 
 rfm_sq|312  0.455      -0.787     0.215  -3.660  < .001 ***
 rfm_sq|313  0.452      -0.794     0.215  -3.692  < .001 ***
 rfm_sq|314  0.448      -0.803     0.212  -3.783  < .001 ***
 rfm_sq|315  0.361      -1.019     0.224  -4.552  < .001 ***
 rfm_sq|321  0.247      -1.399     0.244  -5.745  < .001 ***
 rfm_sq|322  0.380      -0.968     0.221  -4.381  < .001 ***
 rfm_sq|323  0.263      -1.334     0.244  -5.470  < .001 ***
 rfm_sq|324  0.362      -1.015     0.222  -4.569  < .001 ***
 rfm_sq|325  0.269      -1.315     0.241  -5.449  < .001 ***
 rfm_sq|341  0.290      -1.239     0.212  -5.842  < .001 ***
 rfm_sq|342  0.253      -1.376     0.215  -6.384  < .001 ***
 rfm_sq|343  0.167      -1.789     0.244  -7.319  < .001 ***
 rfm_sq|344  0.150      -1.896     0.250  -7.578  < .001 ***
 rfm_sq|345  0.164      -1.807     0.241  -7.485  < .001 ***
 rfm_sq|351  0.127      -2.062     0.261  -7.908  < .001 ***
 rfm_sq|352  0.175      -1.740     0.236  -7.360  < .001 ***
 rfm_sq|353  0.180      -1.713     0.234  -7.318  < .001 ***
 rfm_sq|354  0.120      -2.118     0.265  -7.999  < .001 ***
 rfm_sq|355  0.140      -1.967     0.253  -7.763  < .001 ***
 rfm_sq|411  0.510      -0.674     0.247  -2.727   0.006 ** 
 rfm_sq|412  0.474      -0.746     0.255  -2.922   0.003 ** 
 rfm_sq|413  0.475      -0.744     0.249  -2.986   0.003 ** 
 rfm_sq|414  0.211      -1.556     0.321  -4.848  < .001 ***
 rfm_sq|415  0.341      -1.076     0.271  -3.965  < .001 ***
 rfm_sq|421  0.233      -1.456     0.304  -4.786  < .001 ***
 rfm_sq|422  0.227      -1.482     0.304  -4.875  < .001 ***
 rfm_sq|423  0.182      -1.705     0.330  -5.163  < .001 ***
 rfm_sq|424  0.277      -1.282     0.291  -4.399  < .001 ***
 rfm_sq|425  0.154      -1.872     0.355  -5.277  < .001 ***
 rfm_sq|441  0.164      -1.807     0.294  -6.143  < .001 ***
 rfm_sq|442  0.193      -1.647     0.282  -5.831  < .001 ***
 rfm_sq|443  0.150      -1.899     0.301  -6.308  < .001 ***
 rfm_sq|444  0.147      -1.920     0.309  -6.210  < .001 ***
 rfm_sq|445  0.101      -2.294     0.352  -6.516  < .001 ***
 rfm_sq|451  0.125      -2.081     0.328  -6.348  < .001 ***
 rfm_sq|452  0.116      -2.157     0.339  -6.360  < .001 ***
 rfm_sq|453  0.105      -2.249     0.339  -6.639  < .001 ***
 rfm_sq|454  0.164      -1.807     0.294  -6.143  < .001 ***
 rfm_sq|455  0.057      -2.865     0.436  -6.564  < .001 ***
 rfm_sq|511  0.307      -1.181     0.258  -4.578  < .001 ***
 rfm_sq|512  0.115      -2.162     0.369  -5.862  < .001 ***
 rfm_sq|513  0.214      -1.540     0.283  -5.438  < .001 ***
 rfm_sq|514  0.200      -1.612     0.303  -5.320  < .001 ***
 rfm_sq|515  0.151      -1.893     0.318  -5.944  < .001 ***
 rfm_sq|521  0.137      -1.985     0.354  -5.609  < .001 ***
 rfm_sq|522  0.082      -2.505     0.438  -5.719  < .001 ***
 rfm_sq|523  0.134      -2.013     0.370  -5.444  < .001 ***
 rfm_sq|524  0.014      -4.269     1.013  -4.216  < .001 ***
 rfm_sq|525  0.108      -2.223     0.411  -5.413  < .001 ***
 rfm_sq|531  0.000     -13.483   120.126  -0.112   0.911    
 rfm_sq|532  0.000     -13.483   124.839  -0.108   0.914    
 rfm_sq|533  0.059      -2.829     1.020  -2.773   0.006 ** 
 rfm_sq|534  0.056      -2.887     1.020  -2.832   0.005 ** 
 rfm_sq|535  0.109      -2.213     0.734  -3.014   0.003 ** 
 rfm_sq|541  0.049      -3.017     0.436  -6.921  < .001 ***
 rfm_sq|542  0.049      -3.011     0.436  -6.908  < .001 ***
 rfm_sq|543  0.067      -2.699     0.366  -7.365  < .001 ***
 rfm_sq|544  0.055      -2.898     0.408  -7.110  < .001 ***
 rfm_sq|545  0.023      -3.766     0.597  -6.308  < .001 ***
 rfm_sq|551  0.071      -2.644     0.367  -7.212  < .001 ***
 rfm_sq|552  0.080      -2.525     0.351  -7.191  < .001 ***
 rfm_sq|553  0.033      -3.425     0.523  -6.551  < .001 ***
 rfm_sq|554  0.042      -3.177     0.473  -6.721  < .001 ***
 rfm_sq|555  0.042      -3.177     0.473  -6.721  < .001 ***

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Pseudo R-squared: 0.066
Log-likelihood: -9960.957, AIC: 20141.914, BIC: 21072.856
Chi-squared: 1417.262 df(109), p.value < .001 
Nr obs: 35,000

pred <- predict(result, pred_data = bbb)
print(pred, n = 10)

Logistic regression (GLM)
Data                 : bbb 
Filter               : training == 1 
Response variable    : buyer 
Level(s)             : yes in buyer 
Explanatory variables: rfm_sq 
Interval             : confidence 
Prediction dataset   : bbb 
Rows shown           : 10 of 50,000 

 rfm_sq Prediction  2.5% 97.5%
    512      0.037 0.020 0.070
    534      0.019 0.003 0.120
    443      0.048 0.029 0.078
    251      0.086 0.063 0.117
    453      0.034 0.019 0.061
    254      0.066 0.046 0.094
    555      0.014 0.006 0.033
    114      0.215 0.168 0.270
    111      0.253 0.204 0.310
    354      0.039 0.026 0.059

bbb <- store(bbb, pred, name = "predict_logit")

visualize(
  bbb, 
  xvar = "rfm_sq", 
  yvar = "predict_logit", 
  type = "bar", 
  labs = list(
    y = "Predicted purchase probability", 
    x = "Logistic regression with Sq. RFM"
  ),
  data_filter = "training == 0",
  custom = TRUE
) +
  geom_hline(aes(yintercept = breakeven)) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1))

---
output:
  html_notebook:
    highlight: textmate
    theme: spacelab
    toc: yes
    code_folding: hide
---

```{r r_setup, include = FALSE}
## initial settings
knitr::opts_chunk$set(
  comment = NA,
  echo = TRUE,
  error = TRUE,
  cache = FALSE,
  message = FALSE,

  dpi = 144,
  warning = FALSE
)

## width to use when printing tables etc.
options(
  width = 250,
  scipen = 100,
  max.print = 5000,
  stringsAsFactors = FALSE
)

## make all required libraries available by loading radiant package if needed
if (!exists("r_environment")) library(radiant)

## include code to load the data you require
## for interactive use attach the r_data environment
# attach(r_data)
```

<style>
.table {
  width: auto;
}
ul, ol {
  padding-left: 18px;
}
pre, code, pre code {
  overflow: auto;
  white-space: pre;
  word-wrap: normal;
  background-color: #ffffff;
}
</style>

## RFM for Bookbinders

Loading the data ...

```{r}
bbb <- readr::read_rds("data/bbb.rds")
register("bbb")
```

### Assessing recency

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "last", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Months since last purchase (last)"
  ),
  custom = FALSE
) 
```

Creating the `recency` variable `rec_iq` using the following command in _Data > Transform_:

    rec_iq = xtile(last, 5)

```{r}
## create new variable(s)
bbb <- mutate(bbb, rec_iq = xtile(last, 5))
```

Does recency predict purchase? Are the best customers in quintile 1? The graph below shows this is indeed the case.

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "rec_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Recency quintiles (rec_iq)"
  ),
  custom = FALSE
) 
```

### Assessing frequency

Plots shows that purchase probility is NOT highest in the 1st quantile for frequencey (`purch`).

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "purch", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Purchase frequency (purch)"
  ),
  custom = FALSE
) 
```

This means we need to 'flip' the bin numbers so the highest purchase probility is in the 1st bin (quantile). The easiest way to do this is to add `rev = TRUE` in the call to `xtile`. 

    freq_iq = xtile(purch, 5, rev = TRUE)

Alternatively, you could use:

    freq_iq = 6L - xtile(purch, 5)

```{r}
## bin variables
bbb <- mutate(bbb, freq_iq = xtile(purch, 5, rev = TRUE))
```

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "freq_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Frequency quintiles (freq_iq)"
  ),
  custom = FALSE
) 
```

Why are there only 4 values? Looking at the histogram below we see that the distribution of `purch` is heavily skewed (to the right). This makes it difficult to create 5 _bins_ of similar size

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(bbb, xvar = "purch", color = "freq_iq")
```

### Assessing monetary value

The plot shows that purchase probility is NOT highest in the 1st quantile for `monetary` (`total`)

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "total", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Monetary value (total)"
  ), 
  custom = TRUE
) + 
  theme(axis.ticks = element_blank(), axis.text.x = element_blank()) 
```

Just like we did for `frequency` we have to 'flip' quantiles so the highest purchase probility is in the 1st quantile (i.e., add `rev = TRUE`)

    mon_iq = xtile(total, 5, rev = TRUE)

```{r}
## bin variables
bbb <- mutate(bbb, mon_iq = xtile(total, 5, rev = TRUE))
```

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "mon_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Monetary value quantiles (mon_iq)"
  ),
  custom = FALSE
)
```

## Create the RFM index

Use _Data > Transform > Create_ to generate the RFM index

    rfm_iq = paste0(rec_iq, freq_iq, mon_iq)
    
```{r}
## create new variable(s)
bbb <- mutate(bbb, rfm_iq = paste0(rec_iq, freq_iq, mon_iq))
```

```{r fig.width = 10.5, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "rfm_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Independent RFM index (rfm_iq)"
  ),
  custom = TRUE
) + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  geom_hline(yintercept = 1/9)
```

## Generate  sequential N-tile

```{r}
## create new variable(s)
bbb <- group_by(bbb, rec_iq) %>% 
  mutate(freq_sq = xtile(purch, 5, rev = TRUE)) %>% 
  ungroup()

## create new variable(s)
bbb <- group_by(bbb, rec_iq, freq_sq) %>% 
  mutate(mon_sq = xtile(total, 5, rev = TRUE)) %>% 
  ungroup()
```

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "freq_sq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Frequency quintiles (freq_sq)"
  ),
  custom = FALSE
) 
```

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "freq_sq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Frequency quintiles (freq_sq)"
  ),
  custom = FALSE
) 
```

```{r fig.width = 7, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "mon_sq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Monetary value quintiles (mon_sq)"
  ),
  custom = FALSE
) 
```

## Generate Sequential RFM index

Use _Data > Transform > Create_ to generate the RFM index

    rfm_sq = paste0(rec_iq, freq_sq, mon_sq)
 
```{r}
## create new variable(s)
bbb <- mutate(bbb, rfm_sq = paste0(rec_iq, freq_sq, mon_sq))
```

```{r fig.width = 10.5, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "rfm_sq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'",
    x =  "Sequential RFM index (rfm_sq)"
  ),
  custom = TRUE
) + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1))  +
  geom_hline(yintercept = 1/9)
```

## Resonse rate without RFM

```{r}
result <- explore(
  bbb, 
  vars = "buyer", 
  fun = c("n_obs", "mean", "min", "max")
)
summary(result, top = "fun", dec = 4)
```

## Break-even (aggr)

`r breakeven = 1 / 9`

The breakeven value is `r format_nr(breakeven, dec = 2, perc = TRUE)`. All cells above the breakeven line in the plot below will be mailed.

```{r fig.width = 10.5, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "rfm_iq", 
  yvar = "buyer", 
  type = "bar", 
  labs = list(
    y = "Proportion of buyer = 'yes'", 
    x = "Independent RFM index (rfm_iq)"
  ),
  custom = TRUE
) + 
  geom_hline(aes(yintercept = breakeven)) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1))
```

## Resonse rate

Now that we are creating variables to use in targeting we should use the `training` variable. 

Create the `mailto_iq` variable for independent RFM

    mailto_iq = mean(buyer == "yes") > 1/9

```{r}
## mail TRUE or FALSE
bbb <- group_by(bbb, rfm_iq) %>% 
  mutate(mailto_iq = (sum(training == 1 & buyer == "yes") / sum(training == 1)) > breakeven) %>% 
  ungroup()

## also calculate response rate per group as an illustration
bbb <- group_by(bbb, rfm_iq) %>% 
  mutate(rfm_iq_resp = sum(training == 1 & buyer == "yes") / sum(training == 1)) %>% 
  ungroup()
```

```{r}
result <- pivotr(
  bbb, 
  cvars = c("mailto_iq", "training"), 
  fun = "n_obs", 
  normalize = "column"
)
summary(result, dec = 2, perc = TRUE)
```

```{r}
result <- explore(
  bbb, 
  vars = "buyer", 
  byvar = c("training", "mailto_iq"), 
  fun = c("n_obs", "mean")
)
summary(result, dec = 4)
```

## Calculate profits and ROME

```{r}
dat <- filter(bbb, training == 0)
perc_mail = mean(dat$mailto_iq)
nr_mail = 500000 * perc_mail
rep_rate <- filter(dat, mailto_iq == TRUE) %>% 
  summarize(rep_rate = mean(buyer == "yes")) %>%
  pull("rep_rate")
nr_resp = nr_mail * rep_rate 
mail_cost = 1 * nr_mail 
profit = 9 * nr_resp - mail_cost
ROME = profit / mail_cost
```

Based on independent RFM the number of customers BBB should mail is `r format_nr(nr_mail, dec = 0)` (`r format_nr(perc_mail, perc = TRUE)`). The response rate for the selected customers is predicted to be `r format_nr(rep_rate, perc = TRUE)` or `r format_nr(nr_resp, dec = 0)` buyers. The expected profit is `r format_nr(profit,"$", dec = 0)`. The mailing cost is estimated to be `r format_nr(mail_cost, "$", dec = 0)` with a ROME of `r format_nr(ROME, perc = TRUE)`  


## Repsonse rate with sequential RFM

Create the `mailto_sq` variable for sequential RFM

    mailto_sq = mean(buyer == "yes") > 1/9

```{r}
## mail TRUE or FALSE
bbb <- group_by(bbb, rfm_sq) %>% 
  mutate(mailto_sq = (sum(training == 1 & buyer == "yes") / sum(training == 1)) > breakeven) %>% 
  ungroup()

## also calculate response rate per group as an illustration
bbb <- group_by(bbb, rfm_sq) %>% 
  mutate(rfm_sq_resp = sum(training == 1 & buyer == "yes") / sum(training == 1)) %>% 
  ungroup()
```

```{r}
result <- pivotr(
  bbb, 
  cvars = c("mailto_iq", "training"), 
  fun = "n_obs", 
  normalize = "column"
)
summary(result, dec = 2, perc = TRUE)
```

```{r}
result <- explore(
  bbb, 
  vars = "buyer", 
  byvar = c("training", "mailto_iq"), 
  fun = c("n_obs", "mean")
)
summary(result, dec = 4)
```

## Calculate profits and ROME

```{r}
dat <- bbb
perc_mail = mean(dat$mailto_sq)
nr_mail = 500000 * perc_mail
rep_rate <- filter(dat, mailto_sq == TRUE) %>% 
  summarize(rep_rate = mean(buyer == "yes")) %>%
  pull("rep_rate")
nr_resp = nr_mail * rep_rate 
mail_cost_sq = 1 * nr_mail 
profit_sq = 9 * nr_resp - mail_cost_sq
ROME_sq = profit_sq / mail_cost_sq
```

Based on sequential RFM the number of customers BBB should mail is `r format_nr(nr_mail, dec = 0)` (`r format_nr(perc_mail, perc = TRUE)`). The response rate for the selected customers is predicted to be `r format_nr(rep_rate, perc = TRUE)` or `r format_nr(nr_resp, dec = 0)` buyers. The expected profit is `r format_nr(profit_sq,"$", dec = 0)`. The mailing cost is estimated to be `r format_nr(mail_cost_sq, "$", dec = 0)` with a ROME of `r format_nr(ROME_sq, perc = TRUE)`.

Compare this to the main results from independent RFM. The expected profit is `r format_nr(profit,"$", dec = 0)`. The mailing cost is estimated to be `r format_nr(mail_cost, "$", dec = 0)` with a ROME of `r format_nr(ROME, perc = TRUE)`  

## Confirming the break-even response rate

If we select the predicted response rate for both of the rfm indices (i.e., `rfm_iq_resp` and `rfm_iq_resp`), and select a `profit` and `ROME` plot in `Model > Evaluate Classification` you should see the plots below. A visual inspection suggests that profits will be maximized if we target the top 35% of customers (approximately). You already calculated the exact percentages above. You should find that the number you calculated is very similar to the numbers highlighted green in the `performance.xls` file on Dropbox.

```{r fig.width = 6, fig.height = 4, dpi = 244}
result <- evalbin(
  bbb, 
  pred = c("rfm_iq_resp", "rfm_sq_resp"), 
  rvar = "buyer", 
  lev = "yes", 
  qnt = 50, 
  margin = 9, 
  train = "Test", 
  data_filter = "training == 1"
)
summary(result, prn = FALSE)
plot(result, plots = "profit", custom = FALSE)
```

## Using the RFM index in a logistic regression


```{r fig.width = 7, fig.height = 5.38, dpi = 200}
result <- logistic(
  bbb, 
  rvar = "buyer", 
  evar = "rfm_sq", 
  lev = "yes",
  data_filter = "training == 1"
)
summary(result)
pred <- predict(result, pred_data = bbb)
print(pred, n = 10)
bbb <- store(bbb, pred, name = "predict_logit")
```

```{r fig.width = 10.5, fig.height = 4.67, dpi = 200}
visualize(
  bbb, 
  xvar = "rfm_sq", 
  yvar = "predict_logit", 
  type = "bar", 
  labs = list(
    y = "Predicted purchase probability", 
    x = "Logistic regression with Sq. RFM"
  ),
  data_filter = "training == 0",
  custom = TRUE
) +
  geom_hline(aes(yintercept = breakeven)) +
  theme(axis.text.x = element_text(angle = 90, hjust = 1))
```

